By SABC Sport
2nd March 2024
The British number one followed up her win over second seed Beatriz Haddad Maia in the last 16 by knocking out the 2022 runner-up 6-4 6-3.
From trailing 3-1 in the first set, Boulter won nine of the next 10 games in another confident display.
She will climb to a career-high ranking, on the brink of the top 40, following her latest victory.
Vecic, seeded seventh, broke first in the opening set but then allowed Boulter to hit straight back after an error-strewn service game.
Boulter then saved three break points to hold and grabbed a crucial second break for 5-4 before serving out the set.
Two stunning Boulter backhands brought the 27-year-old from Leicester another break at the start of the second, and a subsequent break to love put her in complete control.
Boulter let Vecic claw one break back as she served for the set, but she converted her first match point with a clubbing forehand after the longest rally of the match, wrapping up the victory in an hour and 36 minutes.
"It was an absolute battle in tricky conditions, it was not easy to get any rhythm as we are both big hitters," Boulter said in her on-court interview.
"I got over the line in the first set and played some good stuff in the second."
Boulter will play American Emma Navarro for a place in the final after the third seed defeated Australia's Daria Saville 6-4 6-2 in her quarter-final.